Let n be the normal to an equipotential surface at a point P. The principal radii of

Let ˆn be the normal to an equipotential surface at a point P. The principal radii of curvature of the surface at P are R₁ and R₂. A formula due to George Green relates normal derivatives (∂/∂n ≡ ˆn · ∇) of the potential φ(r) (which satisfies Laplace’s equation) at the equipotential surface to the mean curvature of that equipotential surface

Derive Green’s equation by direct manipulation of Laplace’s equation.

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K = 1 ½ (R₁¹ + R₂¹):